ODE was done on the basis of David Baraff works. As far as I can remember,
(and confirmed right now by reading his thesis, part 1, 2.4 The penalty method)
he considered not to use penalty-based (where constraints are substituted
by penalty forces) equation of motion because of stiffness of resulting
equations of motion.
So, supposing we get a solver that could relatively inexpensively solve
set of such equations what kind of benefit we could obtain? Should we
search for such a solver? And, to triple confusion of the reader and
possibler answerer, why ODE mentions in documentation that stiff systems
are bad?
PS
I read overview of Havoc physics library and they mention that using stiff
springs for ragdolls might be beneficial comparing to constrained ragdolls
(cannot find that overview right now, though).
PPS
It seems that not only ODE is based on Baraff's work. As far as I can see,
everyone and his dog done their physics library that way.